Various configurations of charge pumps, including Series-Parallel and Dickson configurations, rely of alternating configurations of switch elements to propagate charge and transfer energy between the terminals of the charge pump. Energy losses are associated with propagation determine the efficiency of the converter.
Referring to FIG. 1, a single phase Dickson charge pump 100 is illustrated in a step-down mode coupled to a low voltage load 110 and high voltage source 190. In the illustrated configuration, generally the load is driven (on average) by a voltage that is ⅕ times the voltage provided by the source and a current that is 5 times the current provided by the source. The pump is driven in alternating cycles, referred to as cycle 1 and cycle 2, such that the switches illustrated in FIG. 1 are closed in the indicated cycles. In general, the duration of each cycle is denoted T and the corresponding switching frequency F=½T.
FIGS. 2A-B illustrate the equivalent circuit in each of cycles 2 and 1, respectively, illustrating each closed switch as an equivalent resistance R. Each of the capacitors C1 through C4 has equal capacitance C. In a first conventional operation of the charge pump, the high voltage source is a voltage source, for example, a vin=25 volt source, such that the load is driven by vout=5 volts. In operation the voltage across capacitors C1 through C4 are approximately 5 volts, 10 volts, 15 volts, and 20 volts, respectively.
One source of energy loss in the charge pump relates the resistive losses through the switches (i.e., through the resistors R in FIGS. 2A-B). Referring to FIG. 2A, during cycle 2, charge transfers from capacitor C2 to capacitor C1 and from C4 to C1. The voltages on these pairs of capacitors equilibrate assuming that the cycle time T is sufficiently greater than the time constant of the circuit (e.g., that the resistances R are sufficiently small. Generally, the resistive energy losses in this equilibration are proportional to the time average of the square of the current passing between the capacitors and therefore passing to the load 110. Similarly, during cycle 1, capacitors C3 and C2 equilibrate, capacitor C4 charges, and capacitor C1 discharges, also generally resulting in a resistive energy loss that is proportional to the time average of the square of the current passing to the load 110.
For a particular average current passing to the load 110, assuming that the load presents an approximately constant voltage, it can be shown than the resistive energy loss decreases as the cycle time T is reduced (i.e., switching frequency is increased). This can generally be understood by considering the impact of dividing the cycle time by one half, which generally reduces the peak currents in the equilibration by one half, and thereby approximately reduces the resistive energy loss to one quarter. So the resistive energy loss is approximately inversely proportional to the square of the switching frequency.
However, another source of energy loss relates to capacitive losses in the switches, such that energy loss grows with the switching frequency. Generally, a fixed amount of charge is lost with each cycle transition, which can be considered to form a current that is proportional to the switching frequency. So this capacitive energy loss is approximately proportional to the square of the switching frequency.
Therefore, with a voltage source and load there an optimal switching frequency that minimizes the sum of the resistive and capacitive energy losses, respectively reduced with increased frequency and increased with increased frequency.